Information sharing strategy among particles in Particle Swarm Optimization using Laplacian operator

Particle swarm optimization (PSO) has been extensively used in recent years for the optimization of nonlinear optimization problems. Two of the most popular variants of PSO are PSO-W (PSO with inertia weight) and PSO-C (PSO with constriction factor). Typically particles in swarm use information from global best performing particle, gbest and their own personal best, pbest. Recently, studies have focused on incorporating influences of other particles other than gbest. In this paper, we develop a methodology to share information between two particles using a Laplacian operator designed from Laplace probability density function. The properties of this operator are analyzed. Two particles share their positional information in the search space and a new particle is formed. The particle, called as Laplacian particle, replaces the worst performing particle in the swarm. Using this new operator, this paper introduces two algorithms namely Laplace Crossover PSO with inertia weight (LXPSO-W) and Laplace Crossover PSO with constriction factor (LXPSO-C). The performance of the newly designed algorithms is evaluated with respect to PSO-W and PSO-C using 15 benchmark test problems. The empirical results show that the new approach improves performance measured in terms of efficiency, reliability and robustness.